R CicadaFlux Analysis
Cicada Flux Measurements from 2021
Two Questions are developed on how cicada emergene influences soil respiration and carbon fluxes:
1) To what extent do periodical cicada emergence holes influence soil CO2 efflux? Are responses variable across species or mycorrhizal fungal types?
2) What levels of disruption to ecosystem scale respiration can be attributed to periodical cicada emergence hole densities?
Mechanistic hypothesis:
Conceptual model of competing mechansisms influencing soil respiration following cicada emergence. Nymph cicadas form holes aerating soils (a)) increasing aerobic conditions in the soils increasing both autotrophic (Ra) and heterotropic respiration (Rh). Conversely, emergence holes also increase infiltration (b)) reducing CO2 and oxygen diffusion potential creating anaerobic conditions. Subsequent conditions result in elevated CH4 efflux.
Seasonal Trends in soil temperature and moisture
Figure 1: Soil temperature (a)) and moisture (b)) corresponding to soil respiration collars located at base of trees associated with arbuscular mycorrhiza (AM; blue) and ectomycorrhizal (EcM; yellow) fungi. Measurements represent weekly responses as soil respiration measurements were conducted on different days within the same week.
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: SoilT_C ~ Week + Symbiont
## Data: Rs_plots[Rs_plots$Corr_LinFlux <= 6 & Rs_plots$Sit (Number of observations: 211)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## Intercept 19.30 0.09 19.14 19.46 1.00 2540 2681
## Week2021M06M14 -0.69 0.13 -0.93 -0.46 1.00 3126 2706
## Week2021M06M21 -1.67 0.11 -1.87 -1.47 1.00 2898 2643
## Week2021M07M05 1.25 0.11 1.04 1.46 1.00 3023 3050
## Week2021M07M19 2.60 0.13 2.35 2.86 1.00 3255 2812
## Week2021M08M02 -0.18 0.13 -0.43 0.07 1.00 3348 2851
## SymbiontECM -0.09 0.07 -0.23 0.04 1.00 6208 2781
##
## Family Specific Parameters:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.52 0.03 0.47 0.57 1.00 5769 2377
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (Intercept)-(Inte... = 0 0.09 0.07 -0.05 0.23 NA
## Post.Prob Star
## 1 NA
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: SoilVWC_pct ~ Week + Symbiont
## Data: Rs_plots[Rs_plots$Corr_LinFlux <= 6 & Rs_plots$Sit (Number of observations: 210)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## Intercept 40.58 1.30 38.16 43.03 1.00 2564 2919
## Week2021M06M14 -3.34 1.84 -6.71 0.19 1.00 3472 3416
## Week2021M06M21 -5.82 1.63 -8.91 -2.77 1.00 2947 3125
## Week2021M07M05 -5.47 1.69 -8.66 -2.29 1.00 3181 2931
## Week2021M07M19 -8.88 1.97 -12.61 -5.20 1.00 3428 3069
## Week2021M08M02 -9.61 1.90 -13.18 -6.11 1.00 3495 2977
## SymbiontECM -2.15 1.03 -4.10 -0.23 1.00 5384 2810
##
## Family Specific Parameters:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sigma 7.61 0.37 6.95 8.36 1.00 6024 3409
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (Intercept)-(Inte... = 0 2.15 1.03 0.14 4.17 NA
## Post.Prob Star
## 1 NA *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.Soil temperature and moisture among cicada holes
Figure 2: Soil temperature (a)) and moisture (b)) with respect to the number of cicada holes within the soil respiration collars. No significant differences were noted as collars were typically located within 30 cm of each other.
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Corr_LinFlux ~ Week + Symbiont
## Data: Rs_plots[Rs_plots$Corr_LinFlux <= 6 & Rs_plots$Sit (Number of observations: 214)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## Intercept 1.99 0.14 1.73 2.25 1.00 2109 2827
## Week2021M06M14 -0.19 0.20 -0.57 0.19 1.00 3139 2822
## Week2021M06M21 -0.89 0.17 -1.21 -0.56 1.00 2647 2982
## Week2021M07M05 -0.36 0.18 -0.68 -0.02 1.00 2595 3102
## Week2021M07M19 0.06 0.21 -0.34 0.46 1.00 2766 3072
## Week2021M08M02 -0.18 0.20 -0.57 0.20 1.00 3164 3423
## SymbiontECM 0.11 0.12 -0.12 0.32 1.00 6397 3086
##
## Family Specific Parameters:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.83 0.04 0.76 0.92 1.00 5438 2702
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (Intercept)-(Inte... = 0 -0.11 0.12 -0.33 0.13 NA
## Post.Prob Star
## 1 NA
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Corr_LinFlux ~ n_holes * Symbiont + (1 | Site)
## Data: Rs_plots[Rs_plots$Corr_LinFlux <= 6 & Rs_plots$Sit (Number of observations: 214)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Group-Level Effects:
## ~Site (Number of levels: 2)
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.75 0.64 0.07 2.35 1.00 814 1313
##
## Population-Level Effects:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## Intercept 1.34 0.50 0.23 2.33 1.01 1058 1074
## n_holes 0.64 0.14 0.38 0.91 1.00 1811 1854
## SymbiontECM 0.35 0.14 0.08 0.62 1.00 2119 2400
## n_holes:SymbiontECM -0.57 0.24 -1.02 -0.12 1.00 1872 2345
##
## Family Specific Parameters:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.85 0.04 0.77 0.93 1.00 2402 2097
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (Intercept)-(Inte... = 0 -0.35 0.14 -0.63 -0.07 NA
## Post.Prob Star
## 1 NA *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
Figure 3: Soil respiration for cicada holes (a)) and seasonal trends (b)) with respect to the fungal type
## Family: gaussian
## Links: mu = identity; sigma = log
## Formula: Corr_LinFlux ~ asym * exp(scale * SoilT_C)
## scale ~ 1
## asym ~ 1
## sigma ~ 1
## Data: Rs_plots_sum[Rs_plots_sum$Hole_Collar == 0, ] (Number of observations: 18)
## Draws: 4 chains, each with iter = 8000; warmup = 4000; thin = 1;
## total post-warmup draws = 16000
##
## Population-Level Effects:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sigma_Intercept -0.75 0.18 -1.06 -0.39 1.00 3801 4156
## scale_Intercept 0.05 0.03 -0.01 0.11 1.01 1480 1098
## asym_Intercept 0.68 0.44 0.17 1.75 1.01 1486 1097
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Family: gaussian
## Links: mu = identity; sigma = log
## Formula: Corr_LinFlux ~ asym * exp(scale * SoilT_C)
## scale ~ 1
## asym ~ 1
## sigma ~ 1
## Data: Rs_plots_sum[Rs_plots_sum$Hole_Collar == 1, ] (Number of observations: 18)
## Draws: 4 chains, each with iter = 80000; warmup = 40000; thin = 1;
## total post-warmup draws = 160000
##
## Population-Level Effects:
## Estimate Est.Error l-94% CI u-94% CI Rhat Bulk_ESS Tail_ESS
## sigma_Intercept -0.77 0.18 -1.09 -0.40 1.00 3971 2396
## scale_Intercept 0.09 0.04 0.02 0.17 1.00 721 230
## asym_Intercept 0.38 0.31 0.07 1.16 1.00 728 238
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Q10 ~ Treatment
## Data: Q10_data (Number of observations: 2000)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2.72 0.03 2.67 2.77 1.00 3843 2696
## TreatmentNoHoles -0.96 0.04 -1.03 -0.89 1.00 3607 2787
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.83 0.01 0.81 0.86 1.00 3802 3128
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (Intercept)-(Inte... = 0 0.96 0.04 0.89 1.03 NA
## Post.Prob Star
## 1 NA *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.
Figure 4: The soil temperature effects soil respiration (a)) for collars containing cicada holes (Blue) and no cicada holes (burgundy). Collars containing cicada holes are more sensitive to soil temperature (b)) as soil Q10 was significantly different between the two treatments.
Spatially scaling of soil respiration and cicada emergence
Region of interest:
Theortical footprint for cicada respirtation effects at Morgan-Monroe State Forest AmeriFlux site. Buffer represents a 20 m buffer (red polygon) surrounding each pair of soil respiration collars (points).
Mixed effects model for spatial interpolation
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Corr_LinFlux ~ SoilT_C + SoilVWC_pct + n_holes * Symbiont + (1 | Site)
## Data: Rs_plots[Rs_plots$Corr_LinFlux <= 6 & Rs_plots$Sit (Number of observations: 209)
## Draws: 4 chains, each with iter = 40000; warmup = 20000; thin = 1;
## total post-warmup draws = 80000
##
## Group-Level Effects:
## ~Site (Number of levels: 2)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.07 1.03 0.14 3.85 1.00 3212 1413
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -3.10 1.07 -5.25 -0.98 1.00 14632 7739
## SoilT_C 0.24 0.04 0.16 0.31 1.00 52149 34977
## SoilVWC_pct -0.00 0.01 -0.02 0.01 1.00 41459 34153
## n_holes 0.64 0.13 0.39 0.89 1.00 31029 38162
## SymbiontECM 0.34 0.13 0.09 0.59 1.00 37929 46911
## n_holes:SymbiontECM -0.53 0.22 -0.96 -0.11 1.00 24610 34126
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.78 0.04 0.71 0.86 1.00 43287 36966
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Model selection output Model: Corr_LinFlux ~ SoilT_C + SoilVWC_pct + n_holes * Symbiont + (1|Site) ### elpd_diff se_diff #### MEM_Mod2 0.0 0.0
#### MEM_Mod1 -0.1 1.5
#### MEM_Mod3 -2.5 2.3
## [1] 0.1959534## [1] 0.05834767## OGR data source with driver: ESRI Shapefile
## Source: "D:\Dropbox\Projects\Indiana\Data\CicadaFlux\GIS\MMSF_Cicada_Pheno", layer: "PhenoHoles"
## with 120 features
## It has 10 fields
## Integer64 fields read as strings: field_1 Holes_mx Holes_md_m## OGR data source with driver: ESRI Shapefile
## Source: "D:\Dropbox\Projects\Indiana\Data\CicadaFlux\GIS\MMSF_Cicada_Pheno", layer: "PhenoHoles_Dissolve_15"
## with 1 features
## It has 10 fields
## Integer64 fields read as strings: field_1 Holes_mx Holes_md_m
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [inverse distance weighted interpolation]
## [1] "day" "UnqMeas" "Type" "Etime"
## [5] "Tcham" "Pressure" "H2O" "CO2"
## [9] "Cdry" "Tbench" "RH" "Tboard"
## [13] "Vin" "CO2ABS" "H2OABS" "Hour"
## [17] "DOY" "RAWCO2" "RAWCO2REF" "RAWH2O"
## [21] "RAWH2OREF" "OBS" "VCham" "Offset"
## [25] "Area" "VTotal" "ExpFlux" "ExpFluxCV"
## [29] "Exp_dCdt" "ExpR2" "LinFlux" "LinFluxCV"
## [33] "Lin_dCdt" "LinR2" "LinFluxSE" "File"
## [37] "Collar" "LinReg_R2" "CO2_t0" "CO2_t0_LCI"
## [41] "CO2_t0_HCI" "dCdt" "dCdt_LCI" "dCdt_HCI"
## [45] "Site" "Date" "SoilT_C" "SoilVWC_pct"
## [49] "n_holes" "Corr_offset_cm" "Pair" "Species"
## [53] "Symbiont" "Hole_Collar" "Hole_Plot_m2" "Latitude"
## [57] "Longitude" "Altitude" "VCollar" "Corr_VTotal"
## [61] "Corr_LinFlux" "Corr_LinFlux_LCI" "Corr_LinFlux_HCI" "Week"
## [65] "n_holes_f"
## [1] "TIMESTAMP_START" "TIMESTAMP_END" "USTAR_1_1_1"
## [4] "TA_1_1_1" "WD_1_1_1" "WS_1_1_1"
## [7] "FC_1_1_1" "H_1_1_1" "LE_1_1_1"
## [10] "G_2_1_1" "TS_2_1_1" "P_1_1_1"
## [13] "RH_1_1_1" "PA_1_1_1" "CO2_1_1_1"
## [16] "VPD_PI_1_1_1" "SWC_PI_1" "NETRAD_1_1_1"
## [19] "PPFD_IN_1_1_1" "SW_IN_1_1_1" "SW_OUT_1_1_1"
## [22] "LW_IN_1_1_1" "LW_OUT_1_1_1" "H2O_1_1_1"
## [25] "RECO_PI_1_1_1" "PPFD_DIF_1_1_1" "T_SONIC_1_2_1"
## [28] "TA_1_2_1" "TA_1_3_1" "RH_1_2_1"
## [31] "RH_1_3_1" "CO2_1_2_1" "H2O_1_2_1"
## [34] "SW_IN_1_2_1" "SW_OUT_1_2_1" "LW_IN_1_2_1"
## [37] "LW_OUT_1_2_1" "U_SIGMA_1_2_1" "V_SIGMA_1_2_1"
## [40] "W_SIGMA_1_2_1" "T_SONIC_SIGMA_1_2_1" "T_SONIC_1_1_1"
## [43] "T_SONIC_SIGMA_1_1_1" "PPFD_IN_1_1_2" "TA_1_1_2"
## [46] "RH_1_1_2" "WS_1_1_2" "WD_1_1_2"
## [49] "U_SIGMA_1_1_1" "V_SIGMA_1_1_1" "W_SIGMA_1_1_1"
## [52] "T_SONIC_2_1_1" "CO2_2_1_1" "H2O_2_1_1"
## [55] "SW_BC_IN_1_1_1" "SW_BC_OUT_1_1_1" "LW_BC_IN_1_1_1"
## [58] "LW_BC_OUT_1_1_1" "PPFD_BC_IN_1_1_1" "TA_2_1_1"
## [61] "G_2_1_2" "P_2_1_1" "U_SIGMA_2_1_1"
## [64] "V_SIGMA_2_1_1" "W_SIGMA_2_1_1" "T_SONIC_SIGMA_2_1_1"
## [67] "WS_1_2_1" "WD_1_2_1" "WS_2_1_1"
## [70] "WD_2_1_1" "SWC_1_1_1" "SWC_2_1_1"
## [73] "SWC_3_1_1" "SWC_4_1_1" "SWC_5_1_1"
## [76] "SWC_6_1_1" "SWC_1_PI_SD"
##
## Call:
## lm(formula = comp_data$Flux ~ comp_data$Treatment)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5539 -1.5020 -0.2426 1.3615 8.3191
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.6120 0.1560 16.748 <2e-16 ***
## comp_data$TreatmentPreCicada 0.2925 0.2206 1.326 0.186
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.758 on 252 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.006932, Adjusted R-squared: 0.002991
## F-statistic: 1.759 on 1 and 252 DF, p-value: 0.1859##
## Call:
## lm(formula = comp_data$SoilT ~ comp_data$Treatment)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.4249 -5.0518 -0.2734 5.7392 9.5706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.52795 0.52333 23.939 <2e-16 ***
## comp_data$TreatmentPreCicada 0.01079 0.74010 0.015 0.988
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.898 on 252 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 8.433e-07, Adjusted R-squared: -0.003967
## F-statistic: 0.0002125 on 1 and 252 DF, p-value: 0.9884
## Family: lognormal
## Links: mu = identity; sigma = log
## Formula: FC_Md ~ asym * exp(scale * ST_Md)
## scale ~ 1
## asym ~ 1
## sigma ~ 1
## Data: PreCicada_sumz (Number of observations: 366)
## Draws: 3 chains, each with iter = 10000; warmup = 5000; thin = 1;
## total post-warmup draws = 15000
##
## Population-Level Effects:
## Estimate Est.Error l-89% CI u-89% CI Rhat Bulk_ESS Tail_ESS
## sigma_Intercept -1.02 0.04 -1.08 -0.96 1.00 5292 5108
## scale_Intercept 0.11 0.00 0.10 0.12 1.00 4671 5380
## asym_Intercept 0.16 0.01 0.14 0.18 1.00 4567 5225
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Estimate Est.Error Q5.5 Q89
## R2 0.6941538 0.009433892 0.6776104 0.70492
## Family: lognormal
## Links: mu = identity; sigma = log
## Formula: FC_Md ~ asym * exp(scale * ST_Md)
## scale ~ 1
## asym ~ 1
## sigma ~ 1
## Data: Cicada_sumz[Cicada_sumz$FC_Md > 0, ] (Number of observations: 305)
## Draws: 3 chains, each with iter = 10000; warmup = 5000; thin = 1;
## total post-warmup draws = 15000
##
## Population-Level Effects:
## Estimate Est.Error l-89% CI u-89% CI Rhat Bulk_ESS Tail_ESS
## sigma_Intercept -0.62 0.04 -0.68 -0.55 1.00 5782 5261
## scale_Intercept 0.12 0.01 0.11 0.13 1.00 4881 6085
## asym_Intercept 0.12 0.02 0.09 0.15 1.00 4847 5882
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Estimate Est.Error Q5.5 Q89
## R2 0.6019341 0.02491527 0.5582458 0.6299587
## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: Q10 ~ Treatment
## Data: EC_Q10_d (Number of observations: 30000)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3.00 0.00 3.00 3.01 1.00 3477 2951
## TreatmentCicadaYear 0.38 0.00 0.38 0.39 1.00 2690 2495
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 0.22 0.00 0.22 0.22 1.00 1922 1922
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).## Hypothesis Tests for class b:
## Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio
## 1 (Intercept)-(Inte... = 0 -0.38 0 -0.39 -0.38 NA
## Post.Prob Star
## 1 NA *
## ---
## 'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
## '*': For one-sided hypotheses, the posterior probability exceeds 95%;
## for two-sided hypotheses, the value tested against lies outside the 95%-CI.
## Posterior probabilities of point hypotheses assume equal prior probabilities.